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Statistics - Distribution Function Technique

  1. Feb 27, 2012 #1
    1. The problem statement, all variables and given/known data

    (From Probability and Statistical Inference, Hogg and Tanis, Eighth Edition, 5.1-5)

    The p.d.f. of X is [itex]f(x) = \theta x^{\theta - 1}[/itex] for [itex]0<x<1[/itex] and [itex]0<\theta<\infty[/itex]. Let [itex]Y = -2\theta \ln X[/itex]. How is [itex]Y[/itex] distributed?

    2. Relevant equations

    Um... Fundamental Theorem of Calculus?

    3. The attempt at a solution

    So I've actually solved this, it's exponential with [itex]\theta = 2[/itex]. My question is about the answer given in the back of the book: It cryptically says [itex]M(t) = (1-2t)^{-1}[/itex] for [itex]t<1/2[/itex] which is, to my eye, a useless calculation of the moment-generating function. WTF? Why is this here? Ideas?

    Thank you.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 27, 2012 #2
    What's "\"?
     
  4. Feb 27, 2012 #3
    That is a slash. I'm not 100% sure why you ask, but I think maybe it's because you're confused about how to read the 1/2 (one half).
     
  5. Feb 27, 2012 #4
    transformation using the mgf approach?
     
  6. Feb 28, 2012 #5

    Ray Vickson

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    Science Advisor
    Homework Helper


    One way do get a density is to get its MGF and hope you obtain a familiar, recognizable form. The form they gave you IS familiar. Of course, you are free to do the problem some other way.

    RGV
     
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